Strong union-closed sets conjecture in union-intersection form

Let $\mathcal{F}$ be a reduced union-closed family on a set $S$. Union-intersection formulation of the strong union-closed sets conjecture. The average cardinality of unions of ordered pairs of members of $\mathcal{F}$ is not greater than three times the average cardinality of intersections of ordered pairs of members of $\mathcal{F}$.

This is derived in the source as an equivalent reformulation of the strong union-closed sets conjecture.